Classification of convolutional codes

Convolutional codes have the structure of an F[z]-module. To study their properties it is desirable to classify them as the points of a certain algebraic variety. By considering the correspondence of submodules and the points of certain quotient schemes, and the inclusion of these as subvarieties of certain Grassmannians, one has a one-to-one correspondence of convolutional codes and the points of these subvarieties. This classification of convolutional codes sheds light on their structure and proves to be helpful to give bounds on their free distance and to define convolutional codes with good parameters.